James Morrison came close to equalising for Boro just before half-time, after a strong run down the left he flicked the ball past Luke Steele in the Manchester goal, but Lee Lawrence was on hane to deflect the ball wide for a corner.
Boro had vast amounts of possession throughout the second half but failed to make it count, while United always looked threatening on the break.
At 1-0 the second leg next Friday was wide open, but an injury time goal by Ben Collet effectively killed Boro's chances in the return.